Mathematics and Faith
Just how does an abstract discipline like mathematics find
itself mixed up with a notion as difficult to pin down as that
of faith. What is this thing called faith anyway? As far as I
can see, I never saw faith walking around, nor was I ever able
to touch it. As much as I might have wanted a heavy dose of
faith as a Christmas present some years, I do not ever remember
anyone telling me that they just picked me up a nice piece of
faith in the local mall and got a great deal on it. In the
Book of Hebrews of the New Testament of the Bible we read in
Chapter 11, Verse 1: "Now faith is the substance of things hoped
for, the evidence of things unseen." This has always been one of
my favorite Bible verses I guess because of the profound
implications of the statement. Faith has to be one of the
greatest gifts with which God could have endowed man. Yet
faith--in order to grow strong-- is something that needs to be
put into practice regularly, just like any other muscle in the
body. Use it, or lose it, as the saying goes. Faith strengthens
with use while it weakens through desuetude. Faith is simply not
like some other tangible thing that you can get your finger
around. Consequently, to embrace this elusive yet noble grace,
man needs some kind of driver to bring faith to the surface of
existence, a precursor, so to speak, which causes faith to
bubble into one's life and permits easy access to such.
But what is this so-called faith driver and how do we access it
so as to be able to implement faith in our lives? Moreover, how
can mathematics show us that faith is something real and
consequently that God the Creator, as an extension of our faith,
is really out there?
In short, belief is the key driver of faith. For that which we
believe in no longer necessitates proof of its existence. Yet
everything we believe in has required at some time or
another--in some form or another--a giant leap of faith. And
here is where mathematics, faith, and God all tie in together.
Let me explain.
In 1931, a brilliant Austrian mathematician by the name of Kurt
Gödel shocked the mathematical world with his now famous
Incompleteness Theorems. Up to this time, mathematicians were
working feverishly at formalizing the mathematical disciplines
and trying to show that any rigorous mathematical system was
consistent within itself provided that the axioms on which such
system was built were solid. Kurt Gödel rocked this world with
his theorems that showed that within any mathematical system
there were necessarily inconsistencies and that there were
theorems within the system that could neither be proved nor
disproved. His seminal work at one point during his career even
produced a proof which mathematically would validate God's
existence.
>From the above discussion, we are starting to see--albeit
superficially--some connections among mathematics, faith, and
God. Gödel's work helped show that mathematics is one giant leap
of faith. Yet we see evidence of this leap of faith all around
us. Just think of this the next time you go to start your car
and try to ponder the interconnection between mathematics,
science, and the process of igniting the engine. Yes,
mathematics is all around us. Faith has crystallized into
belief.
For me the previous exposition is easy to accept and believe.
Having studied mathematics from the basic to the advanced
levels, I have firmly come to believe that God speaks to us
through mathematics and that His wisdom is strewn throughout the
many realms of this field. Although for some it is impossible to
conceive of an all-knowing power and creator, a dive into the
myriad oceans of mathematics quickly makes one realize that it
is no more difficult to conceive of such a One than to ponder
the complexities and realities of this extraordinary subject.
After all, what is more difficult to conceive of: an infinite
number of infinities or an Almighty? When I first discovered
this fact about the infinity of infinities during Set Theory
class my senior year in college, I was completely mesmerized.
"How could this be?" I mused. Infinity means just
that--infinity. No end in sight; something that goes on forever.
So how could there be more than one? Even millions. Billions? An
infinity of them? Yet strange realities such as these are what
we derive from mathematics. Once these realities become
validated, our faith in mathematics and in a higher being
becomes more real. Faith is evidence or proof of those things we
cannot see. Faith validates that even though we cannot see
something, i.e. God, that that something is still real.
We see and experience applications of mathematics in the real
world everyday. We have automobiles and electricity and
television and the computer, the latter of which has harnessed
the understanding and power of binary arithmetic. We can see
these applications, touch these applications and enjoy these
applications. They are real. Yet the very foundations on which
such applications are built, the axiomatic systems on which all
applications ultimately derive from theorems provable based on
those axioms, are, according to Kurt Gödel's work, based on a
certain degree of faith. The leap from proof to truth, in the
end, is always based on faith.
We turn on the light switch and know without hesitation the
expected result: the light goes on and the room is illuminated.
We have faith in the light going on because we have seen such
faith demonstrated or used time and time again. We no longer
hope for the light to go on as we know it will. The light turns
on because man has harnessed, via a leap of faith, the electrons
that pass through the wire and generate the current necessary to
illuminate the room. The light is the evidence of things (the
electrons) unseen, which through faith we have come to trust and
believe exist. Thus tangible things we enjoy on a daily basis
prove to us that God is no more a stretch of belief for us than
the simple act of expecting the light to go on after flipping
the switch.
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